Have you thought about using furniture board instead of plywood? It will look like the real thing, finish easier and look more authentic to what the object is meant to be. (plywood will always stay like a sheet). You can coax the cracks by getting some "green" pine and drying it out, hell the hardware stores I always go to seem to always have poor quality dregs on the shelves already cracked (or liable to go - look for wide grain spacing on one side) that I usually have to sift through. Where are they when you need them?
Even pine could easily be finished to look exactly like Maz's box!
Getting experimental, you could soak the pine until it absorbs a lot of water, cut the joints and assemble and let it dry out. You might get the shrunken dove tail joint event that way.
I wonder what theatre design tricks there are for something like this? this box looks just like the stuff the theatre people were working on when I did art at university.
